The issue is not simply a matter of whether T-Mobile was well-managed or not. There are a lot of other factors that bear on the matter.
First, bear in mind that T-Mobile USA is a wholly owned subsidiary of Deutsche Telekom, which is much larger than either AT&T or Verizon.
Second, note that, of all the possible 4G technologies, LTE is going to be needed to compete. AT&T and T-Mobile were given the right to market their "enhanced 3G" as "4G," but it's not nearly as fast as full LTE is going to be. Verizon, on the other hand, decided to go straight to LTE instead of adopting the interim "enhanced 3G." Because Verizon is going straight to LTE their deployment is lagging behind the others, but where you can get Verizon's 4G it is way faster than any of the "4G" speeds from the others. And finally, Sprint adopted WiMax instead of LTE because it is the cheapest 4G system. But WiMax has problems with building penetration, and even out in the open can never deliver the speeds that LTE can.
Now, as to AT&T and T-Mobile, each has problems. AT&T is cash-rich, but failed to bid enough at recent FCC auctions, with the result that they lack spectrum to fully deploy LTE. T-Mobile, on the other hand, has plenty of spectrum, but is strapped for cash. As to the latter comment, witness the fact that Deutsche Telekom recently offered their 7,000 US towers for sale-leaseback.
Now, was it mismanagement that caused Deutsche Telekom to become cash-strapped? You can say that if you like, and I won't argue the point. But if you think that is mismanagement, then I will argue that AT&T's being to tight to bid enough on the spectrum auctions was equally bad management.
In the final analysis, we all mess up from time to time. And sometimes the price we pay is high. And the bigger you are the bigger your screw-ups will be, and the higher the price you may have to pay.